# GATE Questions & Answers of Initial and Boundary Value Problems

## What is the Weightage of Initial and Boundary Value Problems in GATE Exam?

Total 2 Questions have been asked from Initial and Boundary Value Problems topic of Differential equations subject in previous GATE papers. Average marks 1.50.

A function n(x) satisfied the differential equation $\frac{{d}^{2}n\left(x\right)}{d{x}^{2}}-\frac{n\left(x\right)}{{L}^{2}}=0$ where L is a constant. The boundary conditions are: n(0)=K and n ( ∞ ) = 0. The solution to this equation is

The solution of the differential equation ${k}^{2}\frac{{d}^{2}y}{d{x}^{2}}=y-{y}_{2}$ under the boundary conditions (i) y = y1 at x = 0 and (ii) y = y2 at x = $\infty$, where k, y1 and y2 are constants, is